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		<P class='majorTitle'>com.wis.math.calc.solvers.RK45 Documentation</P>

        <P><B>Author:</B> <a href='mailto:wisolutions2002@shaw.ca?subject=wisASLibrary  RK45 Class'>Richard Wright</a><BR>
		<B>Last Modified:</B> 01/12/05 02:49:19<HR class='big'>

		<P class='sectionTitle'>Summary</P>
		<P class='ToC'>com.wis.math.calc.solvers.RK45 class:</P>
		<div class='methodsDiv'><a href='#classinfo'>- description</a></div>
<P class='ToC'>com.wis.math.calc.solvers.RK45 Properties:</P><div class='methodsDiv'>
<a href='#$b'>- $b</a><br>
<a href='#$ch'>- $ch</a><br>
<a href='#$ct'>- $ct</a><br>
<a href='#$stepSize'>- $stepSize</a><br>
<a href='#$numEqn'>- $numEqn</a><br>
<a href='#$truncErr'>- $truncErr</a><br>
<a href='#$err'>- $err</a><br>
<a href='#$tol'>- $tol</a><br>
<a href='#$ode'>- $ode</a><br>
<a href='#$tempState'>- $tempState</a><br>
<a href='#$f'>- $f</a><br>
</div><br>
<P class='ToC'>com.wis.math.calc.solvers.RK45 Methods:</P><div class='methodsDiv'>
<a href='# initialize'>-  initialize</a><br>
<a href='# step'>-  step</a><br>
<a href='# setStepSize'>-  setStepSize</a><br>
<a href='# getStepSize'>-  getStepSize</a><br>
<a href='# setTolerance'>-  setTolerance</a><br>
<a href='#getTolerance'>- getTolerance</a><br>
</div><br>

		<HR class='big'>
		<P class='sectionTitle'><A name='classinfo'></A>com.wis.math.calc.solvers.RK45 <I>class</I></P>
		<P> <span class='methodTitle'>version:</span> 1.7</P>
		<P class="methodTitle">description:</P>
		<P>RK45 implements the behaviours of the IODESolver Interface
 -- a Runge-Kutta 4/5 IODE solver with variable step size. Constructs
 the RK45 IODESolver for a system of ordinary differential equations.
 </P>
		<P class="methodTitle">usage:</P> <pre>var inst:RK45 = new RK45(_ode);</pre>

<P> <span class='methodTitle'>parameters:</span>
				<ul>
<li>      _ode  (IODE)  -- the system of differential equations.</li>
</ul>

			<HR class='small'>
			<P class='groupTitle'><A name='properties'></A>com.wis.math.calc.solvers.RK45 Properties:</P>
			<div class='methodsDiv' >


				<P class='methodTitle'><A name='$b'></A><u> $b</u></P>
				<P> (Array)  -- nested constants array.</P>

				<P class='methodTitle'><A name='$ch'></A><u> $ch</u></P>
				<P> (Array)  -- constants array.</P>

				<P class='methodTitle'><A name='$ct'></A><u> $ct</u></P>
				<P> (Array)  -- constants array.</P>

				<P class='methodTitle'><A name='$stepSize'></A><u> $stepSize</u></P>
				<P> (Number)  -- step size.</P>

				<P class='methodTitle'><A name='$numEqn'></A><u> $numEqn</u></P>
				<P> (Number)  -- number of equations in the ode.</P>

				<P class='methodTitle'><A name='$truncErr'></A><u> $truncErr</u></P>
				<P> (Number)  -- estimated error.</P>

				<P class='methodTitle'><A name='$err'></A><u> $err</u></P>
				<P> (Number)  -- maximum error.</P>

				<P class='methodTitle'><A name='$tol'></A><u> $tol</u></P>
				<P> (Number)  -- tolerance minimum.</P>

				<P class='methodTitle'><A name='$ode'></A><u> $ode</u></P>
				<P> (IODE)  -- the system of differential equations.</P>

				<P class='methodTitle'><A name='$tempState'></A><u> $tempState</u></P>
				<P> (Array)  -- temporary state array.</P>

				<P class='methodTitle'><A name='$f'></A><u> $f</u></P>
				<P> (Array)  -- nested state array.</P>
</div>

			<HR class='small'>
			<P class='groupTitle'><A name='methods'></A>com.wis.math.calc.solvers.RK45 Methods:</P>
			<div class='methodsDiv' >


				<P class='methodTitle'><A name=' initialize'></A><u>  initialize</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Initializes the IODE solver. Temporary state and rate arrays
     are allocated. The number of differential equations is
     determined by invoking getState().length on the IODE.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.initialize(_stepSize);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li> _stepSize  (Number)  -- the step size.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> Void.</P>

				<P class='methodTitle'><A name=' step'></A><u>  step</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Steps (advances) the differential equations by the $stepSize.
     The IODESolver invokes the IODE's getRate method to obtain
     the initial state of the system. The IODESolver then advances
     the solution and copies the new state into the state array
     at the end of the solution step.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.step();</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns the step size.
    </P>

				<P class='methodTitle'><A name=' setStepSize'></A><u>  setStepSize</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Sets the step size. The step size may change when the step
     method is invoked.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.setStepSize(_stepSize);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li> _stepSize  (Number)  -- the step size.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> Void.</P>

				<P class='methodTitle'><A name=' getStepSize'></A><u>  getStepSize</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Gets the step size. The stepsize is adaptive and may
     change as the step() method is invoked.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.getStepSize();</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns the step size.
    </P>

				<P class='methodTitle'><A name=' setTolerance'></A><u>  setTolerance</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Sets $tol class property.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.setTolerance(_tol);</pre>
     </P>
<P> <span class='methodAttributesTitle'>parameters:</span><ul>
<li>_tol  (Number)  -- a real number for tolerance.</li>
</ul></P>
<P><span class='methodAttributesTitle'>returns:</span> Void.</P>

				<P class='methodTitle'><A name='getTolerance'></A><u> getTolerance</u></P>
				<P><span class='methodAttributesTitle'>description: </span>
				Gets $tol class property.
     </P>
				<P><span class='methodAttributesTitle'>usage:</span> <pre>inst.getTolerance();</pre>
     </P>
<P><span class='methodAttributesTitle'>returns:</span> (Number)  -- returns $tol class property.
    </P>
</div>

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